Non-monotonic robust H₂fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties

Abstract

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H 2 fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T-S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H 2 fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

“…In the literature of FMB/PFMB control systems, the concept of higherorder Lyapunov function candidate is applied mainly in discrete-time systems [184,185,186,187,188,189,190] but much less in continuous-time systems [191] as the derivative terms of membership functions are far more difficult to be handled in continuous-time systems.…”

Design of Fuzzy Functional Observer-Controller via Higher Order Derivatives of Lyapunov Function for Nonlinear Systems

“…The control objective is to make the augmented FMB functional observer-control system [formed by (22) and 23] asymptotically stable, i.e., x → 0 and e j → 0 ∀j as time t → ∞, by determining the controller gain G j and observer gains N ij , J ij , H ij , and E j .…”

“…Consequently, the HODLF should be combined with FMB control scheme such that general nonlinear systems can be dealt with. In discrete-time FMB control system, the nonmonotonic Lyapunov function [20]- [22] and the multistep Lyapunov function were investigated [23]- [26]. Similar to HODLF, they involve the difference of Lyapunov function in more steps instead of only one step.…”

Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N‐Step‐Ahead Lyapunov‐Krasovskii Functional Approach

“…It has been successfully used for T-S fuzzy model to relax the monotonicity requirement of LF and further reduce the conservatism of the stability criteria, i.e., allowing the LF to increase locally during several sampling periods. Two-sample variation, i.e., ( +2 ) < ( ) [28][29][30], and -sample variation, i.e., ( + ) < ( ) [31][32][33][34][35][36][37], were fully developed for the T-S fuzzy model. Stability analysis and synthesis, robust ∞ controller design, observer-based fuzzy controller design, and output feedback stabilization have been intensively studied.…”